Nadia is 2 times as old as Ishaan. 35 years ago, Nadia was 7 times as old as Ishaan. How old is Ishaan now?
Solution: We can use the given information to write down two equations that describe the ages of Nadia and Ishaan. Let Nadia's current age be $n$ and Ishaan's current age be $i$ The information in the first sentence can be expressed in the following equation: $n = 2i$ 35 years ago, Nadia was $n - 35$ years old, and Ishaan was $i - 35$ years old. The information in the second sentence can be expressed in the following equation: $n - 35 = 7(i - 35)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $i$ , it might be easiest to use our first equation for $n$ and substitute it into our second equation. Our first equation is: $n = 2i$ . Substituting this into our second equation, we get: $2i$ $-$ $35 = 7(i - 35)$ which combines the information about $i$ from both of our original equations. Simplifying the right side of this equation, we get: $2 i - 35 = 7 i - 245$ Solving for $i$ , we get: $5 i = 210.$ $i = 42$.